Simplify the following expression: $r = \dfrac{x^2 - 7x - 8}{x + 1} $
First factor the polynomial in the numerator. $ x^2 - 7x - 8 = (x + 1)(x - 8) $ So we can rewrite the expression as: $r = \dfrac{(x + 1)(x - 8)}{x + 1} $ We can divide the numerator and denominator by $(x + 1)$ on condition that $x \neq -1$ Therefore $r = x - 8; x \neq -1$